4. The Mexican Spare Parts Company (MSPC) is trying to determine how many fabricating machines to buy for its factory. If we define a spare part to be equal to one unit of output, the price of a new fabricating machine is 6000 units of output, and the price of a one year old machine is 5100 units of output. These relative prices are expected to be the same in the future.

The expected future marginal product of fabricating machines, measured in units of output, is 16,500 – 2K, where K is the number of machines in use. There are no taxes of any sort. The real interest rate is 5% per year.

a. What is the user cost of capital? Specify the units in which your answer is measured.

b. Determine the number of machines that will allow MSPC to maximize its profit.

c. Suppose that MSPC must pay a tax equal to 30%

of its gross revenue. What is the optimal number of machines for the company?

d. Suppose that in addition to the 30% tax on revenue described in part (c), the firm can take advantage of a 20% investment tax credit, which allows it to reduce its taxes paid by 10% of the cost of any new machines purchased. What is MSPC’s desired capital stock now? (Hint: An investment tax credit effectively reduces the price of capital to the firm.)